Liberal senator Dean Smith has warned Malcolm Turnbull a failure to listen to the mood of voters will “seal our electoral fate” as he ramps up pressure on the government to support a Senate inquiry into population.

He said there was a “strong appetite” from crossbenchers for the probe and he will meet the Prime Minister this week to push the case for the government to back it.

Senator Smith said it would be a mistake for the government to oppose the proposed year-long inquiry, arguing a key message from the Longman by-election was the need to listen to the concerns of voters.

“A critical lesson from the recent by-election results for the Coalition is the importance of fine tuning its political antennae to ensure we are listening and responding appropriately to the issues importance of daily importance to Australians and their families,” Senator Smith said.

“The population debate is exactly the type of issue the Coalition can use to demonstrate we are genuinely listening to electors. Failing to listen or responding tardily to policy issues will seal our electoral fate.

“I remain strongly of the view the Australian people now earnestly want to have an active voice in shaping our population policy over the medium term and a Senate led inquiry will give them a powerful and historical opportunity to do so.”

More than five Coalition MPs have publicly backed the probe as well as crossbench senators David Leyonhjelm, Fraser Anning and Stirling Griff, while Tim Storer said he would back it as long as it focused on encouraging migrants to his home state of South Australia.